Abstract
Let S be a unital ring in which 2 is invertible, and let \(R=H(S)\) be the quaternion ring over S. In this paper, we characterize the generalized derivations of R and show that every generalized Jordan derivation on R is a generalized derivation. We also consider the question when a derivation (generalized derivation) of a quaternion ring is an inner derivation (generalized inner derivation). In addition, we show that the structures of the center, ideals, and the above-mentioned derivations of the quaternion rings and matrix rings are similar.
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Ghahramani, H., Ghosseiriand, M.N. & Zadeh, .H. Generalized Derivations and Generalized Jordan Derivations of Quaternion Rings . Iran J Sci Technol Trans Sci 45, 305–308 (2021). https://doi.org/10.1007/s40995-020-01046-4
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DOI: https://doi.org/10.1007/s40995-020-01046-4